How do you find the Exponential Function Equation of y=a(b)^x when given two points on a graph?

Answer 1

(x1,y1) and (x2,y2) are the given points

Then

y1 = a*b^(x1) ---> a = y1 * b^(-x1)

y2 = a*b^(x2)

this is a non-linear system

Ex.

The exponential function y = B^x passes through

(0,3)

(2,12)

3 = a*b^0

3 = a

So y = 3*b^x

Then

12 = 3*b^2

4 = b^2

b = 2

So the exponential function is y = 3*2^x